PURPOSE To enhance the rapid assessment of geographic atrophy (GA) across the macula in a single projection image generated from three-dimensional (3D) spectral-domain optical coherence tomography (SD-OCT) scans by introducing a novel restricted summed-area projection (RSAP) technique. METHODS We describe a novel en face GA visualization technique, the RSAP, by restricting the axial projectio...

introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this ...

In this paper, we provide in a general Hilbert space new characterizations of uniform prox-regularity involving outside but sufficiently close points considered sets. We show that the complement prox-regular set is nothing union closed balls with common radius. derive from given equivalent to semiconvexity property its distance function. Various estimates metric projection mapping are also esta...

PURPOSE To display drusen and geographic atrophy (GA) in a single projection image from three-dimensional spectral domain optical coherence tomography images based on a novel false color fusion strategy. METHODS We present a false color fusion strategy to combine drusen and GA projection images. The drusen projection image is generated with a restricted summed-voxel projection (axial sum of t...

In this paper we determine the class of four-dimensional Lorentzian manifolds that can be completely characterized by the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. We introduce the notion of an I-non-degenerate spacetime metric, which implies that the spacetime metric is locally determined by its curvature invariants. By determinin...

Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four dimensional Einstein equations are equivalent to a three dimensional gravitational theory with a SL(2, C)/SO(1, 1) sigma model as the material source. The sigma model is determined by a complex...

Metric learning has become a widespreadly used tool in machine learning. To reduce expensive costs brought in by increasing dimensionality, low-rank metric learning arises as it can be more economical in storage and computation. However, existing low-rank metric learning algorithms usually adopt nonconvex objectives, and are hence sensitive to the choice of a heuristic low-rank basis. In this p...

A study is made of algebraic curves and surfaces in the flag manifold $$\mathbb {F}=SU(3)/T^2$$ , their configuration relative to twistor projection $$\pi $$ from {F}$$ complex projective plane {P}^{2}$$ defined with help an anti-holomorphic involution $$j$$ . This motivated by analogous studies low degree space {P}^3$$ 4-dimensional sphere $$S^4$$ Deformations fibers project real whose metric ...